A plasma-treatment instrument of such a type is known through EP 2 946 641 B1. The cylindrical roller is rotatably supported in the grip housing by two end-pieces. The electrode extends as a cylindrical hollow electrode over the axial length of the roller and is screened off toward the shell surface of the roller by the dielectric. The dielectric in this case exhibits a structuring, by virtue of which air spaces are formed on the shell surface of the roller when the roller is rolled on the surface to be treated, in particular on the skin surface or wound surface of a living being that is to be treated for cosmetic or therapeutic purposes. The electrode and the dielectric may have been designed to be flexible, so that the roller can, to a certain extent, adapt itself to irregularities of the surface to be treated, so that a controlled plasma treatment—such as is needed, in particular, for the treatment of the skin surface of a living being—is made possible that can be managed in metered manner. In the known arrangement, the roller exhibits a single electrode, to which a high a.c. voltage is capable of being connected through the grip housing. The surface to be treated, in particular the skin surface of a living being, acts in this case as reference electrode or ground electrode.